EP0104845B1 - Vorrichtung zum Steuern von Prozessen - Google Patents

Vorrichtung zum Steuern von Prozessen Download PDF

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Publication number
EP0104845B1
EP0104845B1 EP83305430A EP83305430A EP0104845B1 EP 0104845 B1 EP0104845 B1 EP 0104845B1 EP 83305430 A EP83305430 A EP 83305430A EP 83305430 A EP83305430 A EP 83305430A EP 0104845 B1 EP0104845 B1 EP 0104845B1
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Prior art keywords
output
input
transfer function
accordance
signal
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EP83305430A
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French (fr)
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EP0104845A3 (en
EP0104845A2 (de
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Yasuchika Mori
Takashi Shigemasa
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Toshiba Corp
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Toshiba Corp
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • G05B13/045—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance using a perturbation signal

Definitions

  • the present invention relates to a process control apparatus for digitally controlling a process.
  • a transfer function of a process is identified in accordance with an input signal (control variable) to the process and an output signal (controlled variable) therefrom.
  • PID parameters are then determined in accordance with an identified transfer function, thereby controlling the process by using PID parameters.
  • the process is assumed to be a single input/output process when the transfer function is identified.
  • the conventional process control apparatus serves only as a single loop controller having a single control loop.
  • many processes function as multi-input/output processes.
  • Fig. 1 is a block diagram showing the overall configuration of the process control system.
  • the process control system comprises a closed loop control system having a multi-input/output process 10 and a digital PID controller 12.
  • the process 10 has a plurality of controlled variables (process outputs) such as temperature, humidity, pressure, flow rate, etc., and a plurality of control variables (process inputs).
  • Each controlled variable is influenced by the corresponding control variable.
  • each controlled variable may be influenced by other control variables in some cases.
  • the closed loop control system has N control loops. All signals of the control system comprise N-dimensional vectors, respectively.
  • a set-point signal r,(t) and the process output signal y,(t) are respectively supplied to a (+) input terminal and a (-) input terminal of an adder 14.
  • the control error signal e,(t) is sampled to produce a discrete-time control error signal e, * (k) by a sampler 16.
  • the signal e,*(k) is supplied to the digital PID controller 12.
  • a sampling period ⁇ l may vary between loops.
  • k t/ ⁇ i ,.
  • the controller 12 produces a control variable u oi *(k) for controlling each variable to be controlled.
  • the control system receives a persistently exciting identification signal. More particularly, the output u oi *(k) from the controller 12 and an output v,*(k) from an identification signal generator 20 are added by an adder 18 to produce a control signal u, * (k). A control signal u,(t) along a continuous time base is obtained from the control signal u, * (k) through a Oth-order holder 22. The control variable u,(t) is then supplied to the process 10.
  • Fig. 2 shows a closed loop control system of a 2-input/output process.
  • This process has an interference between the inputs and the outputs, and has four transfer functions: transfer functions Gp 11 (s) and Gp 22 (s) of the two main loops and interference transfer functions Gp 21 (s) and Gp 12 (s).
  • Gp 11 (s) and Gp 22 (s) of the two main loops
  • Gp 21 (s) and Gp 12 (s) Note that a transfer function Gp ij (s) indicates a transfer function between a process input signal u j (t) and a process output signal y,(t). Since the process is controlled by four transfer functions, the controller is also controlled by four transfer functions.
  • sampling periods of the sampler are given as ⁇ 1 and ⁇ 2 for the respective loops. Therefore, holders having the periods ⁇ 1 and ⁇ 2 are used, and identification signals v 1 *(k) and v 2 * (k) are used for the respective loops.
  • the process output signal y,(t) from the process 10 is supplied to a sampler 24 which is operated in synchronism with the sampler 16.
  • the sampler 24 samples the process output signal y i (t) and produces a signal y i *(k).
  • the signal u, * (k) and the signal y, * (k) are supplied to a pulse transfer function identifying circuit 26.
  • the identified Z-transfer function G ij (z i -1 ) is supplied to an S-transfer function calculator 28.
  • the Z-transfer function G ij (z i -1 ) is converted to an S-transfer function Gp ij (s).
  • the S-transfer function Gp, j (s) is supplied to a digital PID parameter calculator 30.
  • the parameter calculator 30 receives a mode signal PID/PI for determining the operating mode of the controller 12 and a response shape parameter ⁇ of the reference model.
  • the parameter calculator 30 matches the S-transfer function of the closed loop control system 10 with the S-transfer function of the reference model to obtain the digital PID parameters Kc lj , Ti ij and Td ij . These parameters are supplied to the controller 12.
  • the identification signal v l *(k) is superposed on the signal u ol *(k) of each loop.
  • a maximum period sequence (M-sequence) signal is selected as an identification signal.
  • the M-sequence signal is represented by equation (1): where 127 is the period of the M-sequence signal, AM is the amplitude thereof, and MOD denotes the modulo operation.
  • the dynamic characteristics of the process during the closed loop control can be identified.
  • the Z-transfer function of the process is identified in accordance with the discrete-time process inputs and outputs.
  • equation (3) is substituted into equation (2), and equation (2) is represented by its components, the following is obtained:
  • Equation (4) for the ith process output y i (k) may be rewritten in the following manner:
  • Equation (5) indicates a model for an N-input/one-output process. Therefore, the N-input/N-output process can be represented by a combination of the N-input/one-output process. Reducing fractions to a common denomination in equation (5), the following equation is obtained: for
  • a parameter prediction technique used for identification of the one-input/ output system can also be used for identification of the dynamic characteristics of the multi-input/output system.
  • the Z-transfer function G(z -1 ) of the process is identified by a recursive least square (RLS) algorithm.
  • the Z-transferfunction can be identified by identifying unknown parameters a 1 *,..., a na *, b 11 *, ..., b 1nb1 *,..., b N1 *, ..., b NnbN *, and C 1 *, .. C nc *.
  • the process model can be expressed in accordance with the RLS algorithm.
  • T denotes the transpose.
  • a vector ⁇ (k) and an unknown parameter vector 0(k) are given as follows:
  • the RLS algorithm can be given as follows: where ⁇ (k) is the forgetting factor.
  • the Z-transfer functions G II (z I -1 ), ..., G IN (z I -1 ) for one process output y 1 *(k) are obtained.
  • the identifying circuit 26 repeats the algorithm N times to identify the Z-transfer functions for all process outputs.
  • a recursive extended least square (RELS) algorithm, a recursive maximum likelihood or the like may be used as an unknown parameter prediction technique instead of the RLS algorithm.
  • the vectors ⁇ (k) and ⁇ of the RELS algorithm are given as follows:
  • the dynamic characteristics of process can be identified as the Z-transfer function.
  • the PID control parameters are obtained from the S-transfer function in a manner to be described later.
  • a Z-transfer function G(z -1 ) of the subprocess is defined as follows:
  • the step response x n is aqpproximated by an m-order polynomial as a function of t, so that
  • the denominator coefficient of the S-transfer function Gp(s) can be obtained as follows:
  • the S-transfer function calculator 28 transforms each Z-transfer function G lj (z -1 ) to the S-transfer function Gp lj (s) by the above means.
  • denominator polynomials of the transfer functions Gp, j (s) differ from each other.
  • the denominator polynomials are then reduced to a common denominator to obtain the general transfer function for the multi-input/output processes.
  • the transfer function Gp(s) for the multi-input/output process 10 is obtained as follows:
  • the operation of the digital PID parameter calculator 30 will be described wherein the PID parameters Kc, Ti and Td for the digital PID controller 12 are tuned in accordance with the identified transfer function Gp(s).
  • the closed loop control system is illustrated in Fig. 4.
  • the operations of the PID controller 12 are expressed as follows:
  • equation (39) is a difference operator and corresponds to the well-known differential operator s for a continuous time system.
  • ⁇ i is decreased to zero
  • k/5 becomes k/s
  • k ⁇ l becomes ks.
  • the approximate expression of the PID controller 12 is obtained along a continuous time base as follows. For example, the controller performs the P operation and the sampler and holder are operated with a period of ⁇ i .
  • the controller can be approximated by the expression k(1 - z i -1 )/ ⁇ i s.
  • the sampling frequencies differ in accordance with the loops, so that the following matrices are given:
  • the response shape of the reference model can be easily changed in accordance with the response shape parameter ⁇ l .
  • the response shape parameter ⁇ l can be set independently for each loop, so that the reference model can be set independently for each loop.
  • This parameter ⁇ l is selected in the range between 0 and 1.0.
  • Fig. 5 shows process outputs y, and y 2 when the set-point signal r changes in a stepwise manner.
  • the output y 1 has substantially no overshoot.
  • Fig. 6 shows process outputs y 1 and y 2 when the set-point signal r 2 changes in a stepwise manner.
  • the output y 2 has about 10% overshoot.
  • Equations (55), (50) and (45) are substituted into equation (43) to obtain the following equation:
  • a process control apparatus wherein the dynamic characteristics of the multi-input/output process are identified during the closed loop control, and model matching is performed using the identified dynamic characteristics, thereby automatically tuning the digital PID parameters of the controller. Therefore, the period required for tuning the controller can be shortened, so that the process can be effectively operated. Furthermore, the decoupled reference model is selected in model matching, so that the multi-input/output process having an interference between the inputs and the outputs can be properly controlled since the loops are independently controlled. In addition to these advantages, the response shape of the reference model can be changed in accordance with a change in parameter for each loop. Therefore, a process control apparatus can be applied to all types of process. In the above embodiment, one-input/output processes and a multi-input/output process having no interference are included, so that the apparatus according to the present invention can be readily applied to any type of process.

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  • Engineering & Computer Science (AREA)
  • Health & Medical Sciences (AREA)
  • Artificial Intelligence (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Evolutionary Computation (AREA)
  • Medical Informatics (AREA)
  • Software Systems (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Feedback Control In General (AREA)

Claims (5)

1. Prozeßsteuer- bzw. -regelvorrichtung für einen Eingabe/Ausgabe-Prozeß (10), umfassend
eine digitale PID-Steuer- oder -Reglereinheit (12) zum Steuern (bzw. Regeln) des Prozesses in Übereinstimmung mit PID-Parametern und Regelfehlern als Differenz zwischen der Ausgabe vom Prozeß und dem Sollwertsignal für die Ausgabe,
eine Signalerzeugungseinheit (20) zum Überlagern der Eingabe zum Prozeß mit einem stetig erregenden Identifizier(ungs)signal,
eine Identifiziereinheit (26) zum Identifizieren von Z-Übertragungsfunktionen entsprechend allen Eingabe-zu-Ausgabe-Kombinationen in Übereinstimmung mit der Eingabe zum Prozeß und der Ausgabe vom Prozeß, während das stetig erregende Identifiziersignal der Eingabe überlagert ist,
eine Recheneinheit (28) zum Berechnen einer S-Übertragungsfunktion des Prozesses nach Maßgabe der identifizierten Z-Übertragungsfunktionen und
eine Abstimmeinheit (30) zum Anpassen einer S-Übertragungsfunktion zwischen einem Sollwertsignal für ein Prozeßsteuer- oder -regelsystem und einer Prozeßausgabe, die von einer berechneten S-Übertragungsfunktion erhalten wird, an eine S-Übertragungsfunktion eines entkoppelten Eingabe-Ausgabe-Referenzmodells und zum Abstimmen der PID-Parameter der PID-Reglereinheit in Übereinstimmung mit angepaßten Ergebnissen, dadurch gekennzeichnet, daß die Prozeßsteuer- bzw. -regelvorrichtung für einen N-Eingabe/Ausgabe-Prozeß (10) (mit N = eine positive ganze Zahl nicht kleiner als 2) geeignet ist, wobei jede Ausgabe durch alle Eingaben interferiert wird,
daß die PID-Reglereinheit (12) N x N digitale PID-Regler umfaßt, die angeordnet sind zum Steuern bzw. Regeln des Prozesses nach Maßgabe von PID-Parametern und Regelfehlern als Differenzen zwischen N Ausgaben vom Prozeß und Sollwertsignalen für die N Ausgaben,
die Signalerzeugungseinheit (20) angeordnet ist zum Überlagern von N stetig erregenden Identifiziersignalen zu den N Eingaben zum Prozeß,
die Identifiziereinheit (26) angeordnet ist zum Identifizieren von Z-Übertragungsfunktionen entsprechend allen Eingabe-zu-Ausgabe-Kombinationen in Übereinstimmung mit den N Eingaben zum Prozeß und den N Ausgaben vom Prozeß, während die N stetig erregenden Identifiziersignale den N Eingaben überlagert sind oder werden,
die Recheneinheit (28) angeordnet ist zum Berechnen der S-Übertragungsfunktionen des Prozesses nach Maßgabe der identifizierten Z-Übertragungsfunktionen, und daß
die Abstimmeinheit (30) angeordnet ist zum Anpassen einer S-Übertragungsfunktion zwischen jedem Sollwertsignal für ein Prozeßsteuer- oder -regelsystem und jeder Prozeßausgabe, die durch die Recheneinheit erhalten oder ermittelt wird, an eine S-Übertragungsfunktion eines entkoppelten N-Eingabe/ Ausgabe-Referenzmodells. und angeordnet ist zum Abstimmen der PID-Parameter der PID-Reglereinheit in Übereinstimmung mit angepaßten Ergebnissen.
2. Vorrichtung nach Anspruch 1, dadurch gekennzeichnet, daß die Signalerzeugungseinheit (20) ein Maximalperiodensequenzsignal als Identifizier(ungs)signal erzeugt.
3. Vorrichtung nach Anspruch 1, dadurch gekennzeichnet, daß die Identifiziereinheit (26) die Z-Übertragungsfunktionen in Übereinstimmung mit einem-wkursiven Algorithmus der kleinsten Quadrate identifiziert.
4. Vorrichtung nach Anspruch 1, dadurch gekennzeichnet, daß die Recheneinheit (28) die S-Übertragungsfunktion durch Laplace-Transformierung eines Polynoms berechnet, das durch Annäherung einer Sprungcharakteristik der Z-Übertragungsfunktion erhalten oder ermittelt wurde.
5. Vorrichtung nach Anspruch 1, dadurch gekennzeichnet, daß die Abstimmeinheit (30) ein Referenzmodell enthält, das definiert oder festgelegt ist, um Ansprech- bzw. Charakteristikformparameter zu beinhalten.
EP83305430A 1982-09-25 1983-09-15 Vorrichtung zum Steuern von Prozessen Expired EP0104845B1 (de)

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JP166040/82 1982-09-25
JP57166040A JP2563894B2 (ja) 1982-09-25 1982-09-25 多入出力サンプル値ｐｉｄ制御装置

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EP0104845A3 EP0104845A3 (en) 1985-01-23
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DE3380971D1 (de) 1990-01-18
CA1213020A (en) 1986-10-21
JPS5955503A (ja) 1984-03-30
US4563734A (en) 1986-01-07
EP0104845A3 (en) 1985-01-23
JP2563894B2 (ja) 1996-12-18
EP0104845A2 (de) 1984-04-04
AU543196B2 (en) 1985-04-04

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